A triptycene-based diamine, 1,3,6,8-tetramethyl-2,7-diamino-triptycene (TMDAT), was used for the synthesis of a novel solution-processable polyamide obtained via polycondensation reaction with 4,4′-(hexafluoroisopropylidene)bis(benzoic acid) (6FBBA). Molecular simulations confirmed that the tetrasubstitution with ortho-methyl groups in the triptycene building block reduced rotations around the C–N bond of the amide group leading to enhanced fractional free volume. Based on N2 sorption at 77 K, 6FBBA-TMDAT revealed microporosity with a Brunauer–Emmett–Teller (BET) surface area of 396 m2 g−1; to date, this is the highest value reported for a linear polyamide. The aged 6FBBA-TMDAT sample showed moderate pure-gas permeabilities (e.g., 198 barrer for H2, ~109 for CO2, and ~25 for O2) and permselectivities (e.g., αH2/CH4 of ~50) that position this polyamide close to the 2008 H2/CH4 and H2/N2 upper bounds. CO2–CH4 mixed-gas permeability experiments at 35 °C demonstrated poor plasticization resistance; mixed-gas permselectivity negatively deviated from the pure-gas values likely, due to the enhancement of CH4 diffusion induced by mixing effects.